We present an I/O-efficient algorithm for computing similarity joins based on locality-sensitive hashing (LSH). In contrast to the filtering methods commonly suggested our method has provable subquadratic dependency on the data size. Further, in contrast to straightforward implementations of known LSH-based algorithms on external memory, our approach is able to take significant advantage of the available internal memory: Whereas the time complexity of classical algorithms includes a factor of Nρ, where ρ is a parameter of the LSH used, the I/O complexity of our algorithm merely includes a factor (N/M)ρ, where N is the data size and M is the size of internal memory. Our algorithm is randomized and outputs the correct result with high probability. It is a simple, recursive, cache-oblivious procedure, and we believe that it will be useful also in other computational settings such as parallel computation.
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